Logging while drilling method and apparatus for measuring standoff as a function of angular position within a borehole

ABSTRACT

A method and apparatus for measuring formation characteristics as a function of angular distance segments about the borehole is disclosed. The measurement apparatus includes a logging while drilling tool which turns in the borehole while drilling. Such characteristics as bulk density, photoelectric effect (PEF), neutron porosity and ultrasonic standoff are all measured as a function of such angular distance segments where one of such segments is defined to include that portion of a &#34;down&#34; or earth&#39;s gravity vector which is in a radial cross sectional plane of the tool. The measurement is accomplished with either a generally cylindrical tool which generally touches a down or bottom portion of the borehole while the tool rotates in an inclined borehole or with a tool centered by stabilizer blades in the borehole.

This is a division, of application Ser. No. 08/183,089, filed Jan. 14,1994 U.S. Pat. No. 5,473,158.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to the field of logging while drillingtools. In particular it relates to such tools for measurement offormation characteristics such as bulk density, photoelectric effect(PEF), neutron porosity and borehole caliper by means of ultrasonicmeasurements. Still more particularly, the invention relates toapparatus and methods for making such measurements as a function ofangular position about the borehole as the tool is turning in suchborehole during drilling.

2. Description of the Related Art

U.S. Pat. No. 5,091,644 of Minette describes a method for analyzingformation data with a logging while drilling tool. Such patent describesdividing the cross section of the borehole into two or more sectors.Gamma ray density signals are divided into four quadrants: top, bottom,right and left for operations in deviated boreholes. The gamma raysignals are collected as to their energy level so as to produce energyspectra for each quadrant. The '644 patent indicates that long and shortspaced detectors are used to collect gamma ray count rate data toproduce compensated density measurements.

Each quadrant measurement is combined with the other, either as a simpleaverage or as a weighted average to produce a density valuecharacteristic of the formation. If the borehole has minimal washout,all four compensated density measurements are used. If there isextensive washout, the "bottom and the two side measurements" are usedto calculate density of the formation. If the borehole suffers extremewashout, only the "bottom" measurement is used.

The '644 patent describes error minimization whereby the spine and ribscorrection is obtained for long and short spaced detector gamma rayspectra and an analysis made from quadrant to quadrant so as to minimizerib error. One or more quadrants are selected so as to minimize theerror in arriving at a density value characteristic of the formation.

The '644 patent suggests that the borehole be broken into fourquadrants, bottom, right, top and left. It suggests that suchmeasurements can be made from measurements in the tool itself or frominformation supplied via a communication bus from another tool. Itsuggests that information from an accelerometer or a magnetometer thatis sent to the density tool is sufficient to break such borehole intofour quadrants.

The '644 patent also discloses providing an acoustic caliper inalignment with a density source and detector for determination ofstandoff in from of the detectors at any given time. Such standoffinformation is used to minimize error of the density characterization ofthe formation due to standoff. It is also used to determinecross-sectional divisions of the borehole.

The disclosure of the '644 patent fails to identify a method toaccurately determine a bottom contact point of a logging while drillingtool operating in a deviated borehole so as to accurately haveinformation as to where the bottom of the borehole is as the sensors ofthe tool turn in the borehole.

IDENTIFICATION AND OBJECTS OF THE INVENTION

A primary object of this invention is to provide a logging whiledrilling method and apparatus by which porosity, density and caliper orother measurements may be made as a function of angular position, orangular distance segment, about a deviated borehole with an accuratedetermination of the bottom of the borehole.

Another object of the invention is to provide a logging while drillingmethod and apparatus for determining an indication of lithology of theformation surrounding the borehole as a function of angular position, orangular distance segment, about the borehole.

Another object of the invention is to provide a logging while drillingmethod and apparatus for determining borehole heterogeneity by comparingformation characteristic measurements of one angular distance segment toanother.

SUMMARY OF THE INVENTION

A preferred embodiment of the method and apparatus of the inventionincludes a logging while drilling tool operatively designed forconnection in a downhole drilling assembly above a drill bit. Adirection and inclination sub, a downhole electronics sub, and acommunication sub, as well as surface instrumentation, are alsoprovided.

The logging while drilling tool of the preferred embodiment of theinvention conducts a plurality of recorded measurements as a function ofborehole angular distance segments:

compensated bulk density derived from gamma ray detector count rateenergy level spectra;

photoelectric effect (PEF) derived from gamma ray detector count rateenergy level spectra;

compensated neutron porosity derived from near and far spaced neutrondetector measurements in response to neutrons interacting with theformation; and

borehole size and shape using an ultrasonic sensor.

Although such measurements are preferably made in quadrants, inprinciple, the angular distance segments may be a greater or lessernumber than four and need not be of equal angular distance.

The invention is applicable to a slick tool, that is, a generallycylindrical tool without stabilizer blades, as well as to a tool withstabilizer blades, that is, a stabilized tool. For a slick tooloperating in a deviated borehole, the density of the formation isdetermined from gamma ray counts while the tool is in a down or bottomquadrant or angular distance segment. When the borehole is deviated orhorizontal, the tool touches the bottom portion of the borehole most ofthe time. Consequently, the standoff for density measurements is at aminimum, and approximately constant, allowing a good spine and ribcorrection. A measurement of rotational density derived from astatistical analysis of all density information about the borehole isalso made.

The down vector of the tool is preferably derived first by determiningan angle φ between a vector to the earth's north magnetic pole, asreferenced to the cross sectional plane of a measuring while drilling(MWD) tool and a gravity down vector as referenced in said plane. Thelogging while drilling (LWD) tool includes magnetometers placedorthogonally in a cross-sectional plane which produces an identical Hvector in the logging while drilling tool as measured in the MWD tool.The angle φ is transmitted to the logging while drilling tool therebyallowing a continuous determination of the gravity down position in thelogging while drilling tool. Alternatively, surveys may be performedperiodically by the MWD tool when drilling is temporarily halted to adddrill pipe to the drill string. Quadrants, that is, angular distancesegments, are measured from the down vector.

The angular position of the sensors with respect to the H vector of theLWD tool is continuously updated so that such angular position withrespect to the various angular distance segments is always known.Measurement data of the sensors thus is always correlated with one ofthe angular distance segments. Consequently, measurement data from eachof the sensors is acquired as a function of the time of theirmeasurement and spatially per their quadrant position in the borehole.

A computer with a computer program is provided for density data toaverage the count rate per energy window, per quadrant, and for theentire borehole at each record rate. The record rate is typically 20seconds and is adjustable. An average density for long and short spacingis determined from such data for the entire borehole and for eachquadrant. The spine and ribs compensation technique is applied to derivebulk density and correction factor for the entire borehole and for eachquadrant.

The computer also includes a computer program to determine rotationaldensity around the entire borehole and of each of the quadrants. Thistechnique uses the rotation of the LWD tool to compensate for boreholeeffect. It is used alternatively to the spine and ribs compensationtechnique.

A first method of computing rotational density is provided by which thevariance of the gamma ray count rate data actually measured is comparedwith the variance expected of a circular borehole. A rotationalcorrection factor is determined. A second method is provided by forminga histogram of gamma ray counts, and extracting only the counts when thedetectors touch the formation.

These methods correct the counting rates for the effect of mud betweenthe detector and the formation. This effect can either increase ordecrease the counting rates in the detectors, depending upon themud-formation density contrast.

The invention also permits a determination of whether apparent muddensity is greater or less than apparent formation density byincorporating information from an ultrasonic measurement of standoff perquadrant. If the average gamma ray counts in the quadrant with standoffare higher than the average counts in a quadrant with no standoff, thenapparent formation density is determined to be higher than the apparentmud density. Therefore, a maximum rotational density is computed usingeither of the two methods described above.

If the average counts in a quadrant with standoff are lower than theaverage counts in the quadrant without standoff, then apparent formationdensity is determined to be lower than apparent mud density. Therefore,a minimum rotational density in computed using either of the two methodsdescribed above.

The rotational density technique is applied to derive bulk density andcorrection factor for the entire borehole and for each quadrant.

The preferred embodiment of the invention also includes a computerprogram for analysis of gamma ray count data to determine a lithologyindicator of the formation photoelectric effect (PEF). The energy windowcount rates are analyzed to determine average PEF for the entireborehole and for each quadrant, and rotational PEF for the entireborehole and each quadrant is determined in a manner similar to thatdescribed above for the determination of rotational density.

Like the density, average porosity for the entire borehole and for eachquadrant is determined. A rotational porosity determination is also madefor the entire borehole and for each quadrant in a manner similar tothat of rotational density and rotational PEF.

An ultrasonic sensor measures standoff between the LWD tool and theborehole wall. A histogram of such standoffs is analyzed to determineminimum and maximum standoff per quadrant. From such standoffs ahorizontal diameter, a vertical diameter and a borehole shapedetermination is made. The borehole standoff values per quadrant areused also in the determination of rotational density, as describedabove, and in the compensation of neutron detector data to correctneutron porosity determinations for borehole size.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects, advantages and features of the invention will become moreapparent by reference to the drawings which are appended hereto andwherein like numerals indicate like elements and wherein an illustrativeembodiment of the invention is shown, of which:

FIG. 1 is a schematic illustration of a downhole logging while drilling(LWD) tool connected in tandem with other measuring while drilling (MWD)tools above a drill bit at the end of a drill string of an oil and gaswell in a section of the well which is substantially horizontal;

FIG. 2 is a schematic longitudinal cross section of the LWD tool of theinvention illustrating a neutron source and neutron detectors, a gammaray source and gamma ray detectors and an ultrasonic detector, producingformation neutron data, formation gamma ray data and ultrasonic signaldata, respectively;

FIG. 3A is a schematic longitudinal cross section of a separate MWD toolhaving magnetometers and accelerometers placed along orthogonal x and yaxes of such tool and a computer for generally continuously orperiodically (e.g., at survey times while the drill string is notturning) determining an angle φ between an H vector and a G vector in aplane of such x and y axes; and further schematically illustrates adownhole electronics module associated with the LWD tool, theillustration showing orthogonal magnetometers placed along x and y axeswhich are in a plane parallel to the plane of the corresponding axes inthe MWD tool;

FIG. 3B is a schematic illustration of computer programs in a downholecomputer for determining borehole quadrants, sensor position, and fordetermining bulk density and rotational density, average PEF androtational PEF, neutron porosity and rotational neutron porosity for theentire borehole and each quadrant, and ultrasonic standoff for eachquadrant;

FIG. 4A illustrates a cross sectional view taken along line 4--4 of FIG.1 showing a generally cylindrical (not stabilized) tool rotating in aninclined borehole, where the borehole has been divided into four equallength angular distance segments-(quadrants) and where the sensor is ina down or bottom position;

FIG. 4B illustrates a similar cross sectional view as that of FIG. 4Abut shows a LWD tool with stabilizing blades such that there issubstantially no difference in standoff from the cylindrical portion ofthe tool to the borehole wall as the tool rotates, and also furthershowing an example of heterogeneous formations with the borehole havingone formation on one side and another formation on the other side, wherethe borehole may be inclined or substantially vertical;

FIG. 5A schematically illustrates magnetometers and accelerometersplaced along x, y and z axes of a MWD tool, with a computer acceptingdata from such instruments to produce an instantaneous angle φ between avector of H¹ of H_(x) and H_(y) and a vector G¹ of G_(x) and G_(y) ;

FIG. 5B illustrates a cross section of the MWD tool showing the angle φas measured from the H¹ vector which is constant in direction, but withtime has different x and y coordinates while the MWD tool rotates in theborehole;

FIG. 6A is an illustration of the magnetometer section andQuadrant/Sensor Position Determination computer program of theelectronics module of FIGS. 3A and 3B, such illustration showing thedetermination of the angle θ of the vector H¹ in terms of the H_(x) andH_(y) signals from the magnetometers in the electronics module, andfurther showing the determination of the angle of a down vector D as afunction of θ(t) and the angle φ transferred from the MWD tool, suchillustration further showing the determination of quadrants as afunction of the angle of the down vector, and such illustration furthershowing the determination of which quadrant that a sensor is in as itrotates in a borehole;

FIGS. 6B-6E illustrate angles from the x and y axes of the LWD tool andfrom the sensors to the H vector as the LWD tool is turning as afunction of time in the borehole;

FIG. 6F illustrates dividing the borehole into four segments, where abottom segment or quadrant is defined about the down vector D;

FIG. 7 illustrates long and short spaced gamma ray detectors withapparatus for accumulating count rates in soft and hard energy windows;

FIG. 8 illustrates a computer program of the LWD computer fordetermining the number of count rate samples per quadrant in hardwindows and in soft windows as well as the total count rate samples forboth the long and short spaced gamma ray detectors, acquisition timesamples and count rates;

FIG. 9 illustrates a computer program of the LWD computer fordetermining the long and short spacing densities, the bulk density andΔρ correction factor determined by a spine and ribs technique for theentire borehole and for each of the bottom, right, top and leftquadrants;

FIGS. 10Aa and 10Ab illustrate a computer program of the LWD computerfor determining rotational density output and Δρ_(ROT) correctionfactors;

FIG. 10B illustrates a LWD tool rotating in an inclined borehole;

FIG. 10C illustrates count rates per quadrant where such count rates arefluctuating from quadrant to quadrant;

FIG. 10D illustrates an example of the entire borehole distribution ofthe number of samples as a function of count rate for the inclined holeof FIG. 10B and for an expected distribution of count rates for acircular borehole, and by way of illustration for a particular quadrantQ_(TOP), the method of determining Δρ_(ROT) and ρ_(b) ROT for the entireborehole and for each quadrant;

FIGS. 11A and 11B illustrate a computer program in the LWD computer fordetermining the average photoelectric effect (PEF) for the entireborehole and for each of the quadrants;

FIGS. 12A-C illustrate a computer program in the LWD computer fordetermining rotational photoelectric effect (PEF) outputs for the entireborehole and for each quadrant;

FIGS. 12D-F illustrate an alternative computer program which may be usedin the LWD computer for determining rotational photoelectric effect(PEF) outputs for the entire borehole and for each quadrant;

FIG. 13 illustrates a computer program in the LWD computer which acceptsstandoff data from the ultrasonic sensor and determines average, maximumand minimum standoff for each quadrant, and determines the horizontaland vertical diameters of the borehole so as to determine the holeshape;

FIGS. 14A and 14B illustrate a computer program in the LWD computer fordetermination of average neutron porosity, as corrected of standoff, forthe entire borehole and for each quadrant; and

FIGS. 15A-C illustrate a computer program in the LWD computer fordetermination of rotational neutron porosity for the entire borehole andfor each quadrant.

DESCRIPTION OF THE PREFERRED EMBODIMENT Introduction

FIG. 1 illustrates a logging while drilling (LWD) tool 100 connected intandem with a drilling assembly including drill bit 50. An associateddownhole electronics module 300 and MWD tool 200 including magnetometersand accelerometers are also connected in tandem with LWD tool 100.Module 300 may be a separate "sub" or it may be disposed in the body ofLWD tool 100. A communication sub 400 is also provided as illustrated inthe drilling assembly.

The LWD tool 100 is shown for illustration purposes as being in aninclined portion of a borehole at the end of a drill string 6 whichturns in a borehole 12 which is formed in formation 8 by penetration ofbit 50. A drilling rig 5 turns drill string 6. Drilling rig 5 includes amotor 2 which turns a kelly 3 by means of a rotary table 4. The drillstring 6 includes sections of drill pipe connected end-to-end to thekelly 3 and turned thereby. The MWD tool 200, electronics module 300 andthe LWD tool 100 and communication sub 400 are all connected in tandemwith drill string 6. Such subs and tools form a bottom hole drillingassembly between the drill string 6 of drill pipe and the drill bit 50.

As the drill string 6 and the bottom hole assembly turn, the drill bit50 forms the borehole 12 through earth formations 8. Drilling fluid or"mud" is forced by pump 11 from mud pit 13 via stand pipe 15 andrevolving injector head 7 through the hollow center of kelly 3 and drillstring 6, and the bottom hole drilling assembly to the bit 50. Such mudacts to lubricate drill bit 50 and to carry borehole cuttings or chipsupwardly to the surface via annulus 10. The mud is returned to mud pit13 where it is separated from borehole cuttings and the like, degassed,and returned for application again to the drill string 6.

The communication sub 400 receives output signals from sensors of theLWD tool 100 and from computers in the downhole electronics module 300and MWD tool 200. Such communications sub 400 is designed to transmitcoded acoustic signals representative of such output signals to thesurface through the mud path in the drill string 6 and downhole drillingassembly. Such acoustic signals are sensed by transducer 21 in standpipe15, where such acoustic signals are detected in surface instrumentation14. The communication sub 400, including the surface instrumentationnecessary to communicate with it, are arranged as the downhole andsurface apparatus disclosed in U.S. Pat. No. 4,479,564 and U.S. Pat. No.4,637,479, which patents are incorporated herein by reference.

The communication sub 400 may advantageously include the communicationapparatus disclosed in U.S. Pat. No. 5,237,540. Such patent is assignedto the assignee of this application and is incorporated herein byreference.

LWD Tool, MWD Tool and Electronics Module

1. LWD Tool

FIG. 2 illustrates in a schematic way the LWD tool 100 of thisinvention. The physical structure of the LWD tool body and associatedsensors is substantially like that described in U.S. Pat. No. 4,879,463to Wraight, et al., and U.S. Pat. No. 5,017,778 to Wraight. Both of suchpatents are assigned to the assignee of the invention described herein.Such patents are incorporated herein for this description of a loggingwhile drilling tool, specifically a compensated density neutron toolused in logging while drilling measurements of formationcharacteristics. LWD tool 100 hardware as shown in FIG. 1 herein isdifferent in at least two respects: (1) an ultrasonic sensor 112 isadded to the assembly and (2) stabilizer blades are not illustrated asbeing provided for LWD tool 100. The provision of stabilizer blades is,however, an alternative embodiment of the LWD tool 100 as shown in FIG.4B, where a stabilized tool is used with methods of the invention asdescribed below.

The LWD tool 100 includes a source of neutrons 104 disposed axially, andnear and far spaced neutron detectors 101,102. It also includes a sourceof gamma rays 106 and short and long spaced gamma ray detectors 108,110. Such LWD tool 100 also includes an ultrasonic transducer 112 formeasuring tool standoff from the borehole wall. Such ultrasonictransducer and system is described in U.S. Pat. No. 5,130,950 in thename of Orban, et al., and is also assigned to the assignee of theinvention described herein. This patent is also incorporated byreference for its detailed description of an ultrasonic sensor 112 ofthe LWD tool 100 of this invention.

2. MWD Tool

A MWD tool 200 is provided in the bottom hole drilling assembly asschematically indicated in FIG. 1. FIG. 3A schematically illustratesthat MWD tool 200 includes magnetometers 201,202 oriented along x and yaxes of the tool. Such x and y axes are in the plane of a radial crosssection of the tool. A z axis of the tool is oriented along itslongitudinal axis. In a similar way, accelerometers G_(x) and G_(y) ofaccelerometer package 208 (which also includes an accelerometer alongthe z axis of the tool) are oriented along the x and y axes of the tool.A microcomputer 210 responds to H_(y) and H_(x) signals and G_(x) andG_(y) signals to constantly determine an angle φ between an H¹ vectorand the G¹ vector, in the cross sectional plane of MWD tool 200. The H¹vector represents that portion of a vector pointed to earth's magneticnorth pole which is projected onto the x--y plane of MWD tool 200. TheG¹ vector represents the down component in the cross sectional plane ofMWD tool 200, of the earth's gravity vector. As illustrated in FIG. 3B,a signal representative of such angle φ is constantly communicated todownhole computer 301 of electronics module 300. Its use in determininga down vector of electronics module 300 and LWD tool 100 is described inthe description of a Quadrant/Sensor Position Determination computerprogram 310 presented below.

3. Electronics Module

The electronics module 300 (which, at the option of a designer, may bepart of MWD tool 200 or an independent sub) of FIG. 3A includes amagnetometer section 302 and a microcomputer 301. The x and y axes, onwhich magnetometers of the magnetometer section 302 are oriented, are ina plane which is substantially parallel with the plane of such axes ofthe MWD tool 200. Accordingly, the H¹ vector generated by themagnetometer section 302 of electronics module 300 is substantially thesame vector H determined by computer 210. Accordingly, the computerprogram 310 has information to determine the down vector angle withrespect to a sensor vector as a function of time. A more detaileddescription of such determination is presented below.

Electronics module 300 receives data from near and far spaced neutrondetectors 101 and 102, short and long spaced gamma ray detectors 108,110 and ultrasonic transducer 112. Ultrasonic transducer 112 isangularly aligned with gamma ray detectors 108, 110 and with gamma raysource 106.

As illustrated in FIG. 3B, downhole computer 301 includes not only theQuadrant/Sensor Position Determination program 310, but also a dataacquisition program 315, a bulk density program 320, a rotationaldensity per entire borehole and per quadrant program 326, an averagephotoelectric effect (PEF) program 330, a rotational PEF program 335, aneutron porosity program 340, a rotational neutron porosity program 345,and an ultrasonic standoff program 350, and others. Such programstransfer data signals among themselves in certain cases, as describedbelow.

Determination of Down Vector, Angular Distance Segments and AngularPosition of Sensors

1. Determination of Down Vector D with respect to x, y axes

FIGS. 5A, 5B, and 6A-F illustrate the determination of a down vector incomputer 301 (FIG. 3B). FIG. 4A shows the case of an unstabilized LWDtool 100 which, in an inclined borehole, generally constantly touchesthe bottom of the borehole. FIG. 4B illustrates the case of a stabilizedLWD tool 100'.

FIG. 5A illustrates the magnetometers H and the accelerometers Goriented along x, y and z axes of the MWD tool 200. As explained above,an angle φ is constantly computed between the H¹ vector (a constantlydirected vector, in the x-y plane for the H directed vector to earth'smagnetic pole) and a G¹ vector (a constantly directed down vector, inthe x-y plane of a vector G directed to the earth's gravitationalcenter, i.e., the center of the earth). As FIG. 5B illustrates, MWD tool200 is rotating in borehole 12. The x and y axes of the tool 200 arerotating at the angular speed of the drilling string, e.g., 30 to 200revolutions per minute, so the x and y components of the H¹ vector andthe G¹ vector are constantly changing with time. Nevertheless, the H¹and the G¹ vectors point generally in constant directions, because theborehole direction changes slowly with time during the time that it isbeing drilled through subterranean rock formations.

FIG. 6A illustrates the magnetometer section 302 of electronics module300. Magnetometers H_(x) and H_(y) are oriented along x and y axes ofthe electronics module 300. Such x and y axes are in a plane which issubstantially parallel with the plane of such axes of MWD tool 200.Accordingly, the H_(x) and H_(y) signals transmitted from magnetometersection 302 to computer 301 and computer program 310 are used to form aconstantly directed reference with respect to an axis of the module,e.g., the x axis.

As FIGS. 6A-6E illustrate, as the MWD tool 200 rotates in borehole 12,an angle θ(t) is constantly formed between the tool x axis and such H¹vector. The angle θ(t) is determined from the H_(x) and H_(y) signalsfrom magnetometer section 302 of electronics module 300:

Next, the down vector angle, angle D(t) is determined in Quadrant/SensorPosition ##EQU1## Determination program 310, as a function of the x andy axes and time, by accepting the angle from the MWD tool 200. The angleof the down vector is determined in program 310 as,

    angleD(t)=Θ(t)-φ

FIGS. 6B-E illustrate the position of MWD tool 200 and electronicsmodule 300/LWD tool 100 in borehole 12 at several times, t₁, t₂, t₃, t₄as it rotates. The angle θ(t) varies with time, because it is measuredfrom the x axis of the MWD tool 200 (and of the electronics module300/LWD tool 100) to the H vector. The angle φ is constant from the H¹vector to the D vector.

2. Determination of Angular Distance Segments

FIG. 6A further illustrates generation of angular distance segmentsaround the borehole. The term "quadrant" is used to illustrate theinvention where four ninety degree angular distance segments are definedaround the 360° circumference of the MWD tool 200 or the LWD tool 100.Other angular distance segments may be defined, either lesser or greaterin number than four. The angular distance of such segments need notnecessarily be equal.

In a preferred embodiment of the invention however, quadrants aredefined as illustrated in the computer program representation of theQuadrant/Sensor Position Determination program 310. A bottom quadrantQ_(BOT) (t) is defined as extending forty-five degrees on either side ofthe down vector D(t). Left quadrant, Q_(LEFT) (t), top quadrant, Q_(TOP)(t) and right quadrant, Q_(RIGHT) (t) are defined as in FIG. 6A.

3. Determination of Angular Position of Sensors

As FIGS. 6B-E further illustrate, the sensors S (e.g., short and longspaced gamma ray detectors 108, 110, ultrasonic transducer 112 and nearand far spaced neutron detectors 101, 102) are oriented at a known angleα from the x axis. Thus, the angle of the sensor is a constant angle αas measured from the x axis of the electronics module or sub 300.Accordingly, computer program 310 determines which quadrant a sensor isin by comparing its angle from the x axis with the quadrant definitionwith respect to the x axis. For example, sensors S are in Q_(BOT) when αis between θ(t)-φ-45° and θ(t)-φ+45°. Sensors S are in Q_(TOP) when α isbetween θ(t)-.SM.-135° and θ(t)-φ-225°, and so on.

FIG. 6F further illustrates the down vector D and four quadrants,Q_(BOT), Q_(RIGHT), Q_(TOP), and Q_(LEFT) which are fixed in space, butare defined as a function of time with the turning x and y axes of MWDtool 200.

Determination of Bulk Density and Δρ Correction Factors for EntireBorehole and for Quadrants

1. Gamma Ray Data Acquisition by Energy Window, Time and by Quadrant

FIG. 7 is a pictorial representation of gamma rays returning from theformation which are detected by gamma ray detectors. The detectors 108and 110 produce outputs representative of the number of counts perenergy window of the counts as reflected in the number and magnitude ofthe gamma rays detected by detectors 108, 110. Such outputs are directedto analog to digital devices (ADC's) and stored in the memory ofdownhole computer 301. An illustration of the storage of the rates ofsuch counts, as a function of energy windows, is also illustrated inFIG. 7. Certain lower energy windows are designated "soft" windows.Certain higher energy windows are designated "hard" windows asillustrated in FIG. 7.

FIG. 8 illustrates that part of a data acquisition computer program 3 15of computer 301 which accepts counts from the ADC's in response todetectors 108, 110. It also accepts starting times and end times for theaccumulating of the total number of counts in each energy window for (1)the short spaced detector and (2) the long spaced detector as a functionof the entire borehole and for each quadrant. The total acquisition timeis also collected for the entire borehole, that is all counts, and forthe acquisition time for each quadrant. Such outputs are for hard windowcounts as well as soft window counts. Computer program 315 alsocalculates count rates for all samples.

2. Bulk Density and Δρ Correction Determination

FIG. 9 illustrates computer program 320 of downhole computer 301 ofelectronics module 300 which accepts count rate signals of long andshort spaced gamma ray detectors for hard window counts by angulardistance segment (i.e., quadrant). Accordingly, as shown schematicallyin FIG. 9, a sub program 321, called "SPINE AND RIBS" receives digitaldata signals representative of the total hard window count rate for theentire borehole from both the long and short spaced detectors anddetermines long spacing density ρ_(L), short spacing density ρ_(S), bulkdensity ρ_(AVG) and Δρ correction. A spine and ribs correction techniqueis well known in the nuclear well logging art of density logging. Suchcorrection technique is based on a well known correction curve by Wahl,J. S., Tiltman, J., Johnstone, C. W., and Alger, R. P., "The DualSpacing Formation Density Log", presented at the Thirty-ninth SPE AnnualMeeting, 1964. Such curve includes a "spine" which is a substantiallylinear curve relating the logarithm of long spacing detector count ratesto the logarithm of short spacing detector count rates. Such curve ismarked by density as a parameter along the curve. "Ribs" cross the spineat different intervals. Such ribs are experimentally derived curvesshowing the correction necessary for different mudcake conditions.

The spine and ribs computer program is repeated as at 322, 323, 324 and325 to determine long spacing density ρ_(L), short spacing densityρ_(S), bulk density ρ_(AVG) and Δρ correction for each quadrant based onthe hard window count rates of the long and short spaced detectors foreach quadrant.

Determination of Rotational Density ρ_(b) ROT and Δρ_(ROT) Correctionfor Entire Borehole and for Quadrants

FIGS. 10Aa and 10Ab illustrate computer program 326 in downhole computer301 which determines rotational density, called ρ_(b) ROT and Δρ_(ROT)correction for each quadrant and for the entire borehole. The method isdescribed for an entire borehole in U.S. Pat. No. 5,017,778 to Wraight,such patent being incorporated by reference into this specification.Such patent is also described in a paper by D. Best, P. Wraight, and J.Holenka, titled, AN INNOVATIVE APPROACH TO CORRECT DENSITY MEASUREMENTSWHILE DRILLING FOR HOLE SIZE EFFECT, SPWLA 31st Annual LoggingSymposium, Jun. 24-27, 1990.

For the entire borehole, signals representing total hard window countrate samples from the long spaced or, alternatively, the short spacedgamma ray detector, and count rate are transferred from data acquisitioncomputer program 315 (FIG. 8). Long and short spacing densities, ρ_(L)and ρ_(S), are transferred from computer program 320 (FIG. 9). A subprogram 328 determines a theoretical or circular hole standard deviation(or variance), determines a standard deviation of the measured samplesof collected data, and determines a delta count rate, ΔCR, as a functionof the variance between the measured standard deviation and thetheoretical standard deviation of a circular hole. Next, a rotationalbulk density digital signal ρ_(b) ROT is determined. Digital signalsrepresentative of Δρ_(ROT) and ρ_(b) ROT are output.

FIGS. 10B, 10C and 10D illustrate the method. FIG. 10B again shows anunstabilized LWD tool 100 rotating in borehole 12. FIG. 10C illustrateslong spacing or, alternatively, short spacing hard window count rates ofthe LWD tool 100 as a function of time. As indicated in FIG. 10C, thetime that the detector is in various quadrants (or angular distancesegments referenced here as Q₁, Q₂ . . .) is also shown. For a non-roundhole, especially for a nonstabilized tool 100, the count rates fluctuateabout a mean value for each revolution of the tool. In FIG. 10C, eightsamples per revolution are illustrated. Data collection continues for 10to 20 seconds.

FIG. 10D illustrates the method of computer program 328 for determiningρ_(b) ROT and Δρ_(ROT) for the entire borehole. First, a mean (average)and theoretical standard deviation (σ_(theor)) for a normal distributionfrom a circular borehole with a stabilized tool is estimated. Next, ahistogram or distribution of the number of samples versus count ratemeasured (CR) is made and a mean and measured standard deviation(σ_(meas)) for all actual counts collected during an actual acquisitiontime is made. A delta count rate factor ΔCR is determined: ##EQU2##

where A is a constant which is a function of the data sampling rate.

Next the Δρ_(ROT) factor is determined: ##EQU3##

where ds is detector sensitivity.

Finally, the rotational bulk density is determined:

    ρ.sub.b ROT =Dρ.sub.L +Eρ.sub.S +FΔρ.sub.ROT

where D, E, and F are experimentally determined coefficients;

ρ_(L) =long spacing density obtained as illustrated in FIG. 9; and

ρ_(S) =short spacing density obtained as illustrated in FIG. 9.

As indicated in FIGS. 10C and 10D also, such ρ_(b) ROT factor and ΔCRfactor is also determined in the same way for each quadrant, but ofcourse, rather than using all of the samples of FIG. 10C, only thosesamples collected in the Q_(TOP) quadrant, for example, are used in thedetermination. As indicated in FIGS. 10Aa and 10Ab, the Δρ_(ROT) factorand ρ_(b) ROT value are determined, according to the invention, for theentire borehole and for each quadrant.

Determination for Average and Rotational Photoelectric Effect (PEF)Outputs for Entire Borehole and as a Function of Quadrants

1. Determination of PEF_(AVG)

FIGS. 11A and 11B illustrate computer program 330 which determinesphotoelectric effect parameters as, alternatively, a function of shortspaced detector soft window count rate and short spaced detector hardwindow count rate or long spaced detector soft window count rate andlong spaced detector hard window count rate. Using the short spaced orlong spaced detector count rate for the entire borehole and the ρ_(AVG)as an input from computer program 320, the factor ##EQU4##

is determined, where the macroscopic cross-section, ##EQU5##

The terms K, B and C are experimentally determined constants.

In a similar manner, as shown in FIGS. 11A and 11B, the U_(AVG) BOT,U_(AVG) RIGHT, U_(AVG) TOP, and U_(AVG) LEFT are determined from shortspaced or long spaced detector soft and hard window count rates whilethe sensor is in the bottom, right, top and left quadrants,respectively.

2. Determination of Rotational PEF

FIGS. 12A-C illustrate computer program 335 in downhole computer 301.The total soft and hard window count rate distributions from the longspaced or, alternatively, the short spaced gamma ray detector, and thecorresponding count rates are accumulated.

In a manner similar to that described above with regard to thecalculation of rotational density, a ΔCR_(SOFT) factor is determinedfrom the soft count rate distribution, ##EQU6##

where A is a constant which is a function of the data sampling rate.Similarly, a ΔCR_(HARD) is determined from the hard count ratedistribution. Next, macroscopic cross-section, U_(ROT), and PEF_(ROT)factors are determined: ##EQU7## where K, B and C are experimentallydetermined constants, and ##EQU8## where ρ_(b) ROT is determined incomputer program 328 as illustrated in FIGS. 10Aa, 10Ab and 10D.

In a similar manner, the PEF_(ROT) factor for each quadrant is alsodetermined, as illustrated in FIGS. 12A-C.

The PEF is an indicator of the type of rock of the formation.Accordingly, PEF_(AVG) is an indicator of the type of rock, on theaverage, of the entire borehole. The PEF_(AVG) per quadrant is anindicator of the type of rock per each quadrant and hence heterogeneityof the formation. PEF_(ROT) signals, as determined by program 335 (FIGS.12A-C) provide further information as to the kind of rocks of theformation.

An alternative methodology for determining rotational PEF is illustratedin FIGS. 12D-F. The total soft count rate and total hard count rate fromthe long spaced or, alternatively, the short spaced gamma ray detectorare accumulated for a plurality of acquisition time samples. Next, foreach such acquisition time sample, a macroscopic cross section factorU_(t) is determined as a function of acquisition time t: ##EQU9## whereK, B and C are experimentally determined constants.

Next, the standard deviation is determined from the distribution ofU_(t) factors. Finally, a rotational value of photoelectric effect,PEF_(ROT), is determined from the distribution of U_(t) 's. Suchrotational value is determined in a manner similar to that illustratedin FIGS. 10Aa, 10Ab and 10D for the determination of ρ_(b) ROT from adistribution of count rate samples as a function of count rate. Themethodology then proceeds as previously described to a determination ofthe overall PEF_(ROT) and PEF_(ROT) for each quadrant.

Ultrasonic Standoff Determination

As illustrated in FIG. 13, computer program 350 of downhole computer 301determines borehole shape from standoff determinations based onultrasonic signals. As mentioned above, U.S. Pat. No. 5,130,950,incorporated herein by reference, describes the determination ofstandoff. Such standoff, i.e. the distance between the ultrasonic sensorand the borehole wall, is determined as a function of quadrant andcollected for each quadrant.

A distribution of standoff values are collected per quadrant for apredetermined acquisition time. From such distribution, for eachquadrant, an average, maximum and minimum value of standoff isdetermined. From such values, a "vertical" diameter of the borehole,using the average standoff of the bottom quadrant plus the tool diameterplus the average standoff of the top quadrant is determined. The"horizontal" diameter is determined in a similar manner.

Determination of Maximum or Minimum Rotational Density

As described above, rotational density is determined around the entireborehole and for each of the quadrants to compensate for boreholeeffects as an alternative technique to the spine and ribs technique. Theinvention further provides a determination of whether apparent muddensity in the borehole, that is the measured density includingphotoelectric effect, is greater than or less than apparent formationdensity by incorporating information from the ultrasonic measurement ofstandoff per quadrant as described-above with respect to FIG. 13. If theaverage gamma ray counts in a quadrant with standoff (e.g., topquadrant) are higher than the average gamma ray counts in a quadrantwith no standoff (e.g., bottom quadrant), then apparent formationdensity is determined to be higher than apparent mud density. Therefore,a maximum rotational density is determined.

If the average gamma ray counts in a quadrant with standoff (e.g. topquadrant) are lower than the average gamma ray counts in a quadrant withno standoff (e.g. bottom quadrant), then apparent formation density isdetermined to be lower than apparent mud density. Therefore, a minimumrotational density is determined.

Determination of Average Neutron Porosity

FIGS. 14A and 14B illustrate a computer program 340 of downhole computer301 which accepts near and far detector neutron count rates from LWDtool 100. It also accepts horizontal and vertical hole diameter digitalsignals from computer program 350 (FIG. 13 discussed above.) Neutroncount rate is affected by hole diameter. Correction curves for hole sizefor neutron count rates are published in the technical literature.Accordingly, measured near and far neutron count rates are corrected,.in this aspect of the invention; by using correction curves or tablesfor hole size as determined by the ultrasonic sensor and associatedcomputer program 350 as described above. Average porosity determinationfrom program 341 using all borehole counts and compensated for offset ofthe tool from the borehole as a function of quadrants is made in aconventional manner.

In a similar way a porosity digital signal is determined for each of theindividual quadrants from far and near neutron detector count rates perquadrant and from such hole shape data.

Determination of Rotational Neutron Porosity

FIGS. 15A-C illustrate computer program 345 of downhole computer 301which accepts total near and far neutron count rates. Histograms, thatis distributions, are produced from all such count rates during theacquisition time. The standard deviation of each distribution isdetermined. Such standard deviations are used to determine rotationalneutron porosity for the entire borehole and for each quadrant in amanner similar to that described in FIG. 10D for the determination ofrotational bulk density.

Determination of Formation Heterogeneity

FIG. 4B illustrates a borehole which is surrounded not by a homogeneousformation, but by two different rock formations. The methods of thisinvention are ideally suited for accessing the degree of formationheterogeneity which exists about the borehole.

Using density measurements, or porosity measurements as disclosedherein, such signals as associated in each particular one of theplurality of angular distance segments defined by the apparatus of FIG.1 and FIGS. 3A and 3B, and according to computer program 310, a signalcharacteristic of the formations surrounding the borehole, such asdensity, PEF or porosity, is derived for each of the angular distancesegments. Formation heterogeneity is assessed by comparing one signalcharacteristic of the formation from one angular distance segment toanother. Such comparison may take the form of a simple differencing ofsuch characteristic from one segment to another, or it may take the formof determining a statistical parameter such as standard deviation orvariance of a characteristic, such as porosity or density, and comparing(e.g. by differencing) such statistical parameter of one segment withanother.

Information Storage

All of the output digital signals may be stored in mass memory devices(not illustrated) of computer 301 for review and possible furtheranalysis and interpretation when the bottom hole drilling assembly isreturned to the surface. Certain data, limited in amount due to bandwidth limitations, may be transmitted to surface instrumentation via thedrill string mud path from communications sub 400.

Various modifications and alterations in the described methods andapparatus which do not depart from the spirit of the invention will beapparent to those skilled in the art of the foregoing description. Forthis reason, such changes are desired to be included in the appendedclaims. The appended claims recite the only limitation to the presentinvention. The descriptive manner which is employed for setting forththe embodiments should be interpreted as illustrative but notlimitative.

What is claimed is:
 1. A method for determining standoff between alogging while drilling tool and an inclined borehole in which said toolis received, including the steps of,determining a bottom contact pointof said tool which contacts said inclined borehole while said tool isrotating in said borehole; defining a bottom angular distance segment,called SEGMENT_(BOTTOM) of said borehole which includes said bottomcontact point; using an ultrasonic transducer in said tool for measuringstandoff between said tool and said borehole as a function of angularposition of said transducer with respect to said borehole; for apredetermined period of time, recording each measurement value ofstandoff which occurs in said bottom angular distance segment to producea bottom angular distance standoff histogram; and determining a signalproportional to average standoff of said bottom angular distance segmentcalled BOTTOM STANDOFF_(AVG), from said bottom angular distance standoffhistogram.
 2. The method of claim 1 further comprising the step offorsaid predetermined period of time, recording each measurement value ofstandoff which occurs in at least one additional angular distancesegment of said borehole to produce another angular distance standoffhistogram; and determining a signal proportional to average standoff,called ANOTHER STANDOFF_(AVG), from said another angular distancestandoff histogram.
 3. The method of claim 1 whereinsaid bottom angulardistance segment comprises a segment of said borehole which isapproximately bisected by said bottom contact point of said tool; andthree additional angular distance segments called SEGMENT_(RIGHT),SEGMENT_(TOP), and SEGMENT_(LEFT) are defined about said borehole inaddition to said bottom angular distance segment, said method furthercomprising the steps of recording for said predetermined period of time,each measurement value of standoff which occurs in each additionalangular distance segment to produce a histogram of standoff measurementsfor each of said additional angular distance segments; and determiningsignals proportional to average standoff of respective signals calledRIGHT STANDOFF_(AVG), TOP STANDOFF_(AVG), and LEFT STANDOFF_(AVG) fromsaid respective additional angular distance segment histograms.
 4. Themethod of claim 3 wherein shape signals are generated according to thesteps ofdetermining a measured vertical diameter of said borehole as afunction of said BOTTOM STANDOFF_(AVG) and said TOP STANDOFF_(AVG)signals; and determining a measured horizontal diameter of said boreholeas a function of said RIGHT STANDOFF_(AVG) and said LEFT STANDOFF_(AVG)signals.
 5. The method of claim 1 wherein said bottom contact point ofsaid tool which contacts said inclined borehole while said tool isrotating in said borehole is determined according to the steps ofin asub having x, y, z axes corresponding to respective axes of said loggingwhile drilling tool determining an H₁ ¹ vector of H_(x), H_(y) signalsfrom magnetometers oriented along x and y axes orthogonal to a z axisalong the longitudinal axis of said borehole determining a G¹ vector ofG_(x), G_(y) signals from accelerometers oriented along respective x andy axes of said sub, and determining an angle φ between said H₁ ¹ vectorand said G¹ vector, and in said logging while drilling tool determiningan H₂ ¹ vector of H_(x), H_(y) signals from magnetometers oriented alongrespective x and y axes of said tool, transferring said φ signal fromsaid sub to said logging while drilling tool, as said logging whiledrilling tool rotates in said borehole, determining a signalrepresentative of an angle θ(t) between an axis of said cross section ofsaid tool and said H₂ ¹ vector measured with said magnetometers of saidtool, and determining a signal representative of a down vector D(t)which constantly points to said bottom contact point by subtracting saidφ signal from said θ(t) signal.
 6. Apparatus for determining standoffcomprisinga logging while drilling tool designed for operation in aninclined borehole, means for determining a bottom contact point of saidtool which contacts said inclined borehole while said tool is rotatingin said borehole; means for determining the extent of a bottom angulardistance segment, called SEGMENT_(BOTTOM) of said borehole whichincludes said bottom contact point; ultrasonic transducer means disposedin said tool for measuring standoff between said tool and said boreholeas a function of angular position of said transducer with respect tosaid borehole; means for recording, for a predetermined period of time,each measurement value of standoff which occurs in said bottom angulardistance segment to produce a bottom angular distance standoffhistogram; and computer program means for determining a signalproportional to average standoff of said bottom angular distance segmentcalled BOTTOM STANDOFF_(AVG), from said bottom angular distance standoffhistogram.
 7. The apparatus of claim 6 further comprisingmeans forrecording, for said predetermined period of time, each measurement valueof standoff which occurs in at least one additional angular distancesegment of said borehole to produce another angular distance standoffhistogram; and computer program means for determining a signalproportional to average standoff, called ANOTHER STANDOFF_(AVG), fromsaid another angular distance standoff histogram.
 8. The apparatus ofclaim 6 whereinsaid bottom angular distance segment comprises a segmentof said borehole which is approximately bisected by said bottom contactpoint of said tool; and three additional angular distance segmentscalled SEGMENT_(RIGHT), SEGMENT_(TOP), and SEGMENT_(LEFT) are definedabout said borehole in addition to said bottom angular distance segment,said apparatus further comprising means for recording, for saidpredetermined period of time, each measurement value of standoff whichoccurs in each additional angular distance segment to produce ahistogram of standoff measurements for each of said additional angulardistance segments; and computer program means for determining signalsproportional to average standoff of respective signals called RIGHTSTANDOFF_(AVG), TOP STANDOFF_(AVG), and LEFT STANDOFF_(AVG) from saidrespective additional angular distance segment histograms.
 9. Theapparatus of claim 8 further comprisingcomputer program means fordetermining a measured vertical diameter of said borehole as a functionof said BOTTOM STANDOFF_(AVG) and said TOP STANDOFF_(AVG) signals; andcomputer program means for determining a measured horizontal diameter ofsaid borehole as a function of said RIGHT STANDOFF_(AVG) and said LEFTSTANDOFF_(AVG) signals.